Spectral Confonning Model and Its Application

Abstract

It has been observed that finite elem-ent or finite difference models of order n can approximate with fair accuracy less than one-third of the eigenvalues of the underlying continuous system corresponding to the low spectrum. We present a new spectral conforming discrete model that estimates n the lowest eigenvalues of the continuous system with uniform accuracy. The building block of the model is the fundamental inverse eigenvalue problem of reconstructing the chain of a mass-spring system with a prescribed spectrum. We present applications of the model in vibration control of continuous systems by using small-order spectral conformning models, and spectrum estimation of non-uniform systems.